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As mentioned - this is not difficult and is often done by a large number of Sys administrators. However, it is not as effective as many are led to believe. In the users screen, your classification types (Name / Users / description) description will remain the same "Built-in account for administering the computer/domain", so the "bad guy" - if he is alert, will still be able to tell which is the real admin account.

The only thing which could be thought of as a potential problem, would be if someone hardcoded some action, program, script - with the default name "administrator", or used the Domain administrator ID as the owner of a utility, but no one would do that - right? The administrator account should never be used as a working ID.
In general - most of us, who change the built-in account, do so when the machines are first added to the domain.
I've never had any problems, The only thing that I can think of is if there is something that's currently being used that is now hardcoded to the old account name or has set to a specific profile name, the system doesn't do that by any default which I know of, if you look in Services you'll note the SID used by the system; Local System, Network service.

As previously addressed, an experienced hacker can see directly which account is the built-in admin account by looking at its Security Identifier (SID).

Hello Pandita,
While renaming the Administrator account is a good move, it can turn out to
be a lot of work. If you have any services that you configured manually to
use the administrator account, then the changes to the name must be
reflected there as well.
Look out for any failed services after renaming the account- this could be
the reason. I run W2K8 R2 at one place but each time I change the admin
password, I have to reconfigure the Antivirus service.
rnyanzi

There wouldnt be any impact if you would change domain administrator name since, renaming would not make any changes to SID No which would remain same.
One you need to make sure this account is not act as any services account for any process renaming would stop certain services which has dependency.

As a IT system administrator always recommand to change default name of domain administrator for security reason.